A planar collector wall floats in an argon discharge ( ) with and

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Plasma Physics, Ch Waves that need pressure or tension: Langmuir, ion-acoustic, Alfven and magnetosonic

Problem

A planar collector wall floats in an argon discharge (

m_i = 39.95\,\mathrm{u}

) with

T_e = 2.5\,\mathrm{eV}

and

n_{e0} = n_{i0} = 2.0\times10^{16}\,\mathrm{m^{-3}}

. The ions are cold. Take

\tfrac{1}{2}\ln(m_i/2\pi m_e) = 4.7

for argon. ((a)) Find the ion-acoustic speed

c_s = (T_e/m_i)^{1/2}

. ((b)) Find the floating-wall potential below the bulk plasma potential, using the total drop

\left(\tfrac{1}{2}+\tfrac{1}{2}\ln\dfrac{m_i}{2\pi m_e}\right)T_e

. ((c)) Find the ion flux

\Gamma_i = 0.61\,n_{e0}c_s

to the wall and the corresponding ion current density.